This approach is simple and works well enough most of the time, especially at low levels where the damage from a single hit can make a big difference and missing can build tension, but can sometimes lead to boring slogs when results are chains of misses and the influence of any single action is low.

An alternative approach is to add an intermediate degree of success incorporating unintended consequences and complications into intermediate results. The Apocalypse World 2d6 +stat roll is one method like this that is easy to use:

10+ = success

7-9 = mixed

1-6 = it gets worse

This works well but does have a few potential downsides. Using 2d6 means limited scope for adjustment, as +1 makes a big difference and each additional bonus makes an even bigger marginal difference. Consider (probabilities are approximate, taken from Anydice):

While this might seem okay if you like to keep numerical inflation to a minimum anyways, it does, somewhat counterintuitively, make the marginal bonus (the next potential +1) always more influential, in terms of mechanical effectiveness, than the last +1.

2d6 is also incompatible directly with d20 systems.

It is easy enough to create a similar method using 1d20 though, and such yields a uniform distribution, meaning that each marginal +1 has the same impact on resulting probability (+5%).

Here is one approach which has some attractive properties:

19-20 success (10%)

10-18 mixed (45%)

1-9 it gets worse (45%)

Single digits = bad is easy to remember; 19 or higher = extra good is also easy to remember. The outcome ranges could easily interoperate with standard ability or attack bonuses. Bonus increments correspond to 5% probability adjustments, which are easy to reason about.

This differs slightly from the approach taken by the traditional attack roll and similar resolution systems, where the roll, modified by properties of a character such as attack bonus, must attain a threshold determined by some external factor, such as armor class. In contrast, the Apocalypse Word target numbers (and these adapted d20 target numbers) are fixed. If the only modifiers to the roll are character properties such as ability score bonuses or attack bonuses, then this resolution mechanism is essentially solipsistic; the result is unaffected by things external to the character.

This could be an issue if you want success versus a dragon to be less likely than success versus a goblin. Using situational penalties could address this problem, but that way lies the hassle of adding and subtracting a host of potential bonuses or penalties. Used sparingly this works well enough, though it is less than ideal, and anyone that has played Pathfinder or even something like traditional AD&D should be familiar with modifier creep (1d20 + strength bonus + attack bonus + magical weapon bonus – odious magical aura penalty … and so forth). It works mathematically of course, but can be a mess.

Here is another approach, using tiers based on academic letter grades for shorthand:

19-20 = A

16-18 = B

10-15 = C

2-9 = D

1 = F

This adds some complexity at first glance, but also supports slightly more granular outcomes that are also relatively easy to remember, especially 1 = F. The only threshold without an easy to remember association is the transition between C and B results, occurring at 16. Further, now it becomes easy to see how the tiers of this solipsistic resolution system could correspond to properties of a fictional world, if desired, without needing to worry about setting difficulty classes by challenge. For example, results of C hit unarmored opponents, results of B hit lightly armored opponents, and results of A hit heavily armored opponents. More generally, C = easy, B = moderate, and A = hard, assuming easy tasks still represent an uncertain outcome that is potentially consequential either way (otherwise why bother rolling at all?). Or: C = success with setbacks, B = success, and A = extraordinary success.

Ultimately, a graduated outcome like Apocalypse World is probably more interesting than succeed/fail systems (heresy?), so I am tempted to interpreting the roll as follows:

19-20 A = extraordinary success/critical hit/overkill

16-18 B = success

10-15 C = success with complications

2-9 D = it gets worse

1 F = it gets much worse/catastrophe

What about the dragon > goblin issue described above? One could also model this difference through hit point totals and the severity of complications.

This set of outcomes is less sensitive to bonus inflation than 2d6 +stat but would still break with Pathfinder-scale bonuses of +15, so some consideration of bounded accuracy would still be required. Basically, just keep bonuses from growing too large. +10 means that a character would always be at least in the success with complications tier apart from the 5% chance of rolling a natural 1, assuming conventional interpretation of natural 1 results.

1-10-16-19 seems easy enough to remember and has the potential to be universal, applicable to anything that one might normally resolve by rolling a d20. I think I may give this a shot the next time I run something.

Regarding curves, that is true, but is covered indirectly in the discussion of probabilities. There is nothing magical about the different distributions, as they still all boil down to a set of fixed outcome percentages given a particular data generation mechanism, at least in the context of outcome profiles as used in RPG resolution systems.

I hadn’t heard about that 2d20 method before but I like it. I’m not sure how it would integrate with 5E-style advantage or disadvantage rules off the top of my head, but I’m sure that could be sorted out.

You could also look at Talislanta in its various forms. It had something like this, which I’ve always remembered and used sometimes. I like the Apocalypse 2d6 thing because I’ve been tweaking Traveller on and off for decades, quite liked Mongoose’s 1e effort, and liked their ‘quality’ approach. And like Ben Milton’s Maze Rats 2d6 take on Into the Odd. But like the nod to story telling options that partial fail vs partial success can give. I’d suggest trying a modded Talislanta, or grafting something onto a simpler retro clone if you’re afraid of breaking 5e. I don’t know 5e at all so can’t help there.